极限在-1和1之积摆动,极限不存在.
lim(x->0) sin(x²sin(1/x))/x (0/0型)
=lim 2xsin(1/x)cos(x²sin(1/x))-cos(1/x)cos(x²sin(1/x))
=lim 2*0*sin(1/x)cos(0)-cos(1/x)cos(0)
=lim -cos(1/x)
=-cos(∽)
极限不存在!
极限在-1和1之积摆动,极限不存在.
lim(x->0) sin(x²sin(1/x))/x (0/0型)
=lim 2xsin(1/x)cos(x²sin(1/x))-cos(1/x)cos(x²sin(1/x))
=lim 2*0*sin(1/x)cos(0)-cos(1/x)cos(0)
=lim -cos(1/x)
=-cos(∽)
极限不存在!